1 Factorise the expression below using the factor theorem. Use polynomial division to evaluate a quotient and remainder in your method.

and 2Factorise the expression below using the remainder theorem.

Both of these are easy to factorise but when we covered the factor and remainder theorems in class they kind of merged together and I cant work out which is which!

I know that evaluating f(a) gives 0 when (x - a) is a valid factor which you then divide by to get the quotient which is what I have done for the first one, but for the second one I am assuming I have to do the full polynomial division for each trail factor just keeping the ones that factor out to a 0 remainder?

dasy2k1 wrote:1 Factorise the expression below using the factor theorem. Use polynomial division to evaluate a quotient and remainder in your method.

2 Factorise the expression below using the remainder theorem.

...when we covered the factor and remainder theorems in class they kind of merged together and I cant work out which is which!

The Factor Theorem lets you figure out if "x - a" is a factor by making sure that the remainder is 0 when you do the synthetic division (or if you just divide by "x - a" with regular poly division).

The Remainder Theorem lets you evaluate functions by finding their remainder. The value of f(a) is whatever the remainder is when you do the synthetic division by "a". If "a" is a root, then the remainder will be 0.

I don't know how you're supposed to "use the Factor Theorem" in anything other than the way the Remainder Theorem works. Maybe you're supposed to try stuff, doing long division, for #1, but use synthetic division for #2? Are there any examples in your book or in your class notes?